380 
792 
The above empirical equation for sea water 
compressibility is due to Ekman" and has been 
widely used for computation of sound velocity 
in sea water..°!2 The validity of the Ekman 
equation for sound velocity calculations was 
verified experimentally as indicated in Table VII. 
Experimental sound velocity measurements 
were made by recording with a rotating drum 
camera the signals applied to a cathode ray 
oscilloscope by two very small piezoelectric 
gauges placed a known distance apart. The sound 
source was a No. 8 detonator cap placed far 
enough away from the gauges so that the effect 
of finite pressure amplitude was less than 0.03 
percent. An error of about 0.2 percent was in- 
herent in the experimental work owing to slight 
errors in the alignment of the two recording 
gauges with the sound source. This accounts for 
the magnitude and systematic nature of the dis- 
crepancy apparent in Table VII. 
Further verification of the applicability of 
Ekman’s equation in the region up to 1.50 
kilobars is given in Table VIII where values ob- 
tained from the equation are compared with the 
experimental values of Adams for NaCl solutions. 
5. Compressibility Data for Intermediate Pres- 
sure Region (Table II) 
As indicated in Part 1 of this appendix, a sea 
water salinity of 32 parts per thousand cor- 
responds to a 3.79 weight percent solution of 
NaCl. The compressibility of NaCl solution of 
this concentration was obtained by graphical 
interpolation of Adams's data.® 
The Tait equation in the form: 
v(0, T)—v(p, T)/v(0, T) = (1/n) logli+p/B) ], 
t=(T—273.16)°C 
was then fitted to Adams's data. In an effort to 
TABLE IX. Values of » computed from p—v—T data 
(using »=7.15 in computation of AT). 
pe Pp (kg/cm?) 
(°C) 5000 15,000 25,000 
20 7.211 7.183 7.130 
40 7.360 7.126 6.969 
60 7A\1 7.054 6.868 
* t9=centigrade temperature through which the adiabatic for S 
passes at zero pressure. 
uV. W. Ekman, Publications de Circonstance No. 43 
(Conceil Permanent Internationale Pour L’Exploration de 
la Mer. November 1908). 
12 Matthews, Tables of the Velocity of Sound in Pure 
Water and Sea Water for Use in Echo Sounding and Sound 
Ranging (Hydrographic Dept., Admiralty, H.D. No. 282). 
RICHARDSON, ARONS, 
AND HALVERSON 
check the Tait equation against the Ekman 
equation used for computation of Table I, a fit 
was first made to the lower pressure region. 
Values of n and B(25°C) were so selected that the 
equation not only fitted the data of Adams with 
adequate precision but also yielded the correct 
velocity of sound in the limit of zero pressure. 
This additional restriction (that the equation 
give C)=1528 m/sec. at 25°C and s=32) required 
that nB(25°C) = 23.497, the latter relation being 
obtained from the thermodynamic equations: 
(4 Vo" (2) 
Op 2 Co” Cp oT ms 
ov Vo 
(—) =— at p=0. 
Op T nB(t) 
In this case 7 was taken as 7.445 and B(25°C) 
as 3.156 kilobars, and the resulting equation fits 
the data of Adams quite closely up to pressures 
of about 4 kilobars as shown in Table VIII. For 
purposes of further calculation, the temperature 
variation of B was assumed to be the same as that 
used by Kirkwood and Richardson on the basis 
of a private communication from Gibson (see 
Appendix II). Calculation of U—¢o/co at 1.00 
kilobar yielded a value of 7.85 percent, in good 
agreement with the value of 7.81 percent ob- 
tained from the Ekman equation. 
Having verified the accuracy of results ob- 
tained from the Tait equation when fitted as 
described above, the same technique was used to 
fit the equation to the intermediate pressure 
range (up to-values for 11 kilobars quoted by 
Adams; it was assumed safe to extrapolate the 
resulting equation to pressures of 14 or 15 kilo- 
bars). It was found that the best fit of the data 
as well as a correct value for the velocity of 
sound were obtained by taking »=7.800 and 
B(25°C) =3.012, the temperature variation of B 
again being assumed to be that mentioned above. 
The Tait equation containing these parameters 
was then used for the computation of Table II. 
The fit of the equation to Adams’s data is shown 
in Table VIII. 
APPENDIX II 
1. Data Employed in the Computations of Part 
B of Section II 
In the modified Tait equation, Eq. (2.12), the 
function A[.S]=B(t), where t=T[0, S]— 273.16, 
